Question: Solve for $x$ and $y$ using elimination. ${5x-3y = 14}$ ${2x-3y = 2}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-1$ ${-5x+3y = -14}$ $2x-3y = 2$ Add the top and bottom equations together. $-3x = -12$ $\dfrac{-3x}{{-3}} = \dfrac{-12}{{-3}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {5x-3y = 14}\thinspace$ to find $y$ ${5}{(4)}{ - 3y = 14}$ $20-3y = 14$ $20{-20} - 3y = 14{-20}$ $-3y = -6$ $\dfrac{-3y}{{-3}} = \dfrac{-6}{{-3}}$ ${y = 2}$ You can also plug ${x = 4}$ into $\thinspace {2x-3y = 2}\thinspace$ and get the same answer for $y$ : ${2}{(4)}{ - 3y = 2}$ ${y = 2}$